Pith Number

pith:Q5M2ESY5

pith:2026:Q5M2ESY52CVO27O5OWABVUUVVL

not attested not anchored not stored refs pending

Localization and unique continuation for the Anderson-Bernoulli model with long-range hopping on $\mathbb{Z}$

Shihe Liu, Yunfeng Shi, Zhifei Zhang

arxiv:2607.03472 v1 · 2026-07-03 · math.SP · math-ph · math.AP · math.DS · math.MP · math.PR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Q5M2ESY52CVO27O5OWABVUUVVL}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Cited by

1 paper in Pith

Quantitative Unique Continuation on Simplex and $\mathbb{Z}^n$

Receipt and verification

First computed	2026-07-07T02:17:48.589862Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8759a24b1dd0aaed7ddd75801ad295aad550bd28523ac36bc77f1962f08b889a

Aliases

arxiv: 2607.03472 · arxiv_version: 2607.03472v1 · doi: 10.48550/arxiv.2607.03472 · pith_short_12: Q5M2ESY52CVO · pith_short_16: Q5M2ESY52CVO27O5 · pith_short_8: Q5M2ESY5

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/Q5M2ESY52CVO27O5OWABVUUVVL \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 8759a24b1dd0aaed7ddd75801ad295aad550bd28523ac36bc77f1962f08b889a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6c16839e47523f22d6dc511bb9541fa1e197b0eeee2927f40095327ec0cb614c",
    "cross_cats_sorted": [
      "math-ph",
      "math.AP",
      "math.DS",
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2026-07-03T16:33:01Z",
    "title_canon_sha256": "2d59965c45bf3fed17b1ee8ec30adcc89d732f978cd67df22273d88cdf81940d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.03472",
    "kind": "arxiv",
    "version": 1
  }
}